In this study, a 2D numerical model is investigated for removal of CO2 in a hydrophobic polyvinylidene fluoride (PVDF) hollow fiber membrane contactor (HFMC) using the computational fluid dynamics (CFD) method. The model considers axial and radial diffusion in the membrane contactor. It also considers convection in the tube and shell side. The model governing equations were solved with using finite-element method. Simulation predictions were validated with the experimental data obtained from literature for CO2 absorption from the gas mixture by water. The simulation predictions were in good agreement. The results of this model are in good agreement with experimental data CO2 removal from the gas mixture by water. In velocity 5 m/s absorbent fluid removal efficiency carbon dioxide at a constant temperature of 10 and 40 °C, respectively, 55.36 and 46.25 %. In velocity of 5 m/s absorbent fluid and 0.2 m/s gas mixture removal efficiency of carbon dioxide absorbent 51.43 and 23.34 % respectively during counter current and co-current flow. Increasing liquid velocity led to an increase in removal efficiency of carbon dioxide. By increasing the gas mixture velocity, removal efficiency is reduced. It is shown that this method is able to predict the performance of the membrane contactor hollow fiber to absorb CO2 from the gas mixture.